Why did the FTDNATiP™ probability become less when we eliminated the possibility of a common ancestor within the past seven generations? It seems that it should increase?

These are cumulative probabilities. That is the key to understanding something that initially seems counter intuitive.

Let’s use an example for a specific situation of one mismatch in 37 markers. Before inputting your information, the chance of having a common ancestor in the first four generations is 59.03% and chances for having a common ancestor in the next eight generations (between generations four and twelve) is 97.48 minus 59.03 or 38.45% . Now, with the new information that there were no common ancestors in the last seven generations, the chance of having a common ancestor between seven generations ago and eleven generations ago is 75.55%. In other words, this new information not only increased the percentage, but also increased the focusing time from four to eight generations to seven to eleven generations.